Accelerated Volumetric FRONSAC with WAVE and CAIPI
Nadine Luedicke Dispenza1, Robert Todd Constable2,3, and Gigi Galiana4

1Biomedical Engineering, Yale University, New Haven, CT, United States, 2Department of Radiology and Biomedical Imaging, Yale University, New Haven, CT, United States, 3Department of Neurosurgery, Yale University, New Haven, CT, United States, 4Radiology and Biomedical Imaging, Yale University, New Haven, CT, United States


This work demonstrates the potential of FRONSAC, which adds oscillating nonlinear gradients to the Cartesian readout, for 3D accelerated imaging. In undersampled trajectories using either standard Cartesian encoding, CAIPI encoding, or WAVE-CAIPI encoding, significant further improvements are achieved when FRONSAC is applied in addition to these approaches.


FRONSAC, an acceleration strategy to improve undersampled image quality by applying small nonlinear gradient perturbations during the readout, has previously been demonstrated in 2D(1). Since the oscillating nonlinear gradients used in the FRONSAC approach varies spatially in 3 dimensions, it is expected that volumetric FRONSAC images will reduce undersampling artifacts in 2 dimensions.

FRONSAC encoding uses nonlinear gradients to modulate the shape of the sampling function in k-space, and it is distinct from linear trajectories that change the path of the sampling function in k-space. However, the oscillating nonlinear gradients applied during readout make the FRONSAC technique appear similar to WAVE – a technique with slew rate limited low frequency oscillating linear gradients(2). Likewise, the incoherent sampling created by FRONSAC encoding is a feature shared by CAIPI, where the phase encoding of the acquisition is modified to control the aliasing artifacts(3).

In this work, we show that each of these paths through k-space (Cartesian, CAIPI, and WAVE-CAIPI) are further enhanced by the addition of FRONSAC gradients. While CAIPI and WAVE-CAIPI provide a more efficient path through k-space, highly undersampled versions of these trajectories still leave significant gaps in k-space. The addition of nonlinear FRONSAC gradients improves the sampling of gaps in each trajectory, providing the best image quality from a highly undersampled scan.


Figure 1 shows the FRONSAC sequence as applied to a standard 3D Cartesian sequence. All simulations applied this same gradient in addition to the linear gradient encoding prescribed by each linear gradient trajectory. All data was simulated in MATLAB (MathWorks Inc, Natick, Massachusetts, USA) over a 250 mm3 FOV with imaging matrix size 643 and parallel imaging with a 32 channel head coil with Ry=4 and Rz=2. Figure 2 shows a three-plane rendering of coil profiles used in the presented initial simulations. FRONSAC data is simulated by adding 3 oscillating spherical harmonic gradient fields, x3-3xy2, 3yx2-y3 and x2+y2 (commonly known as C3, S3, and Z2), to the readout with maximum C3/S3/Z2 strength = 162.6 mT/m3, 158.3 mT/m3 and 20.8 mT/m2 with oscillation frequency of w0/2pi = 1.6 kHz where C3/Z2 follows a sine waveform and S3 follows a cosine waveform. This corresponds to experimental acquisitions achieved in our scanner for a bandwidth of 130Hz/pix. WAVE-CAIPI linear gradient parameters are matched to the parameters described by Bilgic et al(2).


The first column of Figure 3 shows images reconstructed with standard Cartesian undersampling, a CAIPI trajectory, and finally a WAVE-CAIPI trajectory. These results show that each of these modifications to the linear trajectory significantly improve undersampled image quality and the methods can be combined to further improve the final result. Since each of these sequences only defines the trajectory on the linear gradients, they are further compatible with FRONSAC encoding that improves measurement of k-space in the gaps of each trajectory. This is simulated in the second column of Figure 3, which shows that image quality is always improved by the addition of FRONSAC encoding. The greatest improvement in image quality is seen in a combination of all three strategies: WAVE-CAIPI trajectory with FRONSAC encoding during readout.


For these initial simulations, the limited coil sensitivity in the y direction limits the success of undersampling for all the imaging methods. However, higher resolution simulations with higher coil counts are currently underway. In addition, the FRONSAC gradients simulated here are those chosen for their previous performance in single slice imaging. Current work is exploring modifications in orientation and gradient waveform which will further enhance the performance of FRONSAC encoding for volumetric imaging. Conclusion: FRONSAC is a powerful approach for improving volumetric undersampled image quality and can provide even further image improvements when combined with CAIPI and WAVE techniques.


FRONSAC is a powerful approach for improving volumetric undersampled image quality and can provide even further image improvements when combined with CAIPI and WAVE techniques.


We would like to thank Andrew Dewdney and Terry Nixon for support with the nonlinear gradient hardware.


1. Wang H, Tam LK, Constable RT, Galiana G. Fast rotary nonlinear spatial acquisition (FRONSAC) imaging. Magnetic Resonance in Medicine 2016;75(3):1154-1165.

2. Bilgic B, Gagoski BA, Cauley SF, Fan AP, Polimeni JR, Grant PE, Wald LL, Setsompop K. Wave-CAIPI for highly accelerated 3D imaging. Magn Reson Med 2014.

3. Breuer FA, Blaimer M, Heidemann RM, Mueller MF, Griswold MA, Jakob PM. Controlled aliasing in parallel imaging results in higher acceleration (CAIPIRINHA) for multi-slice imaging. Magnetic Resonance in Medicine 2005;53(3):684-691.


The pulse sequence diagram for a 3D FRONSAC acquisition. Oscillating nonlinear gradients are added during the readout where C3 and Z2 follow a sine waveform while S3 follows a cosine waveform.

The sum of the coil sensitivity profiles measured experimentally with a 32 channel head coil. The limited sensitivity in the y direction is apparent in the sagittal slice.

Compared to an undersampled Cartesian trajectory, both a CAIPI trajectory and a WAVE CAIPI trajectory through k-space reduces undersampling artifacts, as shown in the first column. However, at high undersampling factor, each of these methods leaves significant gaps in k-space. Adding nonlinear FRONSAC encoding to each of these acquisitions, as shown in the second column, further improves undersampling, with the best image quality achieved by a WAVE CAIPI linear trajectory enhanced by nonlinear FRONSAC encoding. All images are undersampled Ry*Rz=4x2.

Proc. Intl. Soc. Mag. Reson. Med. 27 (2019)